Semi-retro-reflection refers to a reflection property of an approximately macroscopically planar structure wherein the planar structure reflects a substantial fraction of the light that strikes it, and does so with a special directional characteristic, especially for incident light that is within a range of directions deviating by less than approximately 45 degrees from the direction perpendicular to the macroscopically planar structure. The special directional characteristic is that for each incident light ray, the reflected light propagates backward in approximately the reverse direction, in other words, back towards the point of origin, with a deviation from the reverse direction that is macroscopically random and primarily less than a predetermined maximum deviation, wherein the predetermined maximum deviation being less than approximately 45 degrees. This semi-retro-reflection exhibits what is often called “optical gain”, meaning that it increases the apparent reflectance of the surface under common illumination and viewing conditions. Furthermore, the manner in which light is reflected from this structure results in a paper-like white appearance. A paper-like white appearance is generally preferable to the metallic luster normally observed in optical systems that exhibit optical gain.
A semi-retro-reflective characteristic can be approximated in a reflective display incorporating an array of convex or hemi-spherical protrusions or hemi-spheres (it should be noted that the terms “convex protrusions” and “hemi-spherical protrusions” and “hemi-spheres” will henceforth be used interchangeably). Depicted in FIG. 1 is a front sheet 100 of a reflective display with an outward front surface 102 facing the viewer and an inward surface 104 comprising of a plurality of hemi-spherical protrusions 106 which reflects light by means of total internal reflection (TIR) within the individual hemi-spheres 108. Typically only about half of the incident light rays on sheet 100 are totally internally reflected, impeding attainment of a white appearance, as depicted in enlarged detail of a portion of a hemi-spherical array in FIG. 2. In the FIG. 2 example, the incident light rays 110 (depicted as solid lines) are either totally internally reflected and emerge as reflected light rays 112 (depicted as dotted lines) back towards the viewer or they pass through the dark pupil region as non-totally reflected light rays 114. The incident light rays 110 deviate by about 30 degrees from the perpendicular direction, which represents a typical operating condition where high quality semi-retro-reflection is desired but not achieved due to the large fraction of light rays 114 that do not undergo total internal reflection within the hemi-spheres largely due to passing through the non-reflective dark pupil region as previously explained, for example, in U.S. Pat. No. 6,885,496.
One approach to recovering a substantial portion of the light rays 114 that pass through the dark pupil region is to place a planar reflective element 116 beneath the hemi-spherical array as shown in FIG. 3 to improve reflectivity. However, although the planar reflector is able to cause most incident light rays 110 (depicted as solid lines) to undergo net reflection, most light rays reflected by the planar reflector do not have the desired semi-retro-reflection characteristic and emerge as light rays 118 (depicted as dotted lines) that instead are reflected away from the viewer and the source of incident light. High optical gain can be achieved by the system shown in FIG. 3 if the incident light rays are incident perpendicular to the hemispherical array's planar outward surface, but this has limited usefulness in practice.
Another approach to reflecting light rays that pass through the dark pupil regions of the individual convex or hemi-spherical protrusions as shown in FIG. 2 but in a semi-retro-reflective manner is to place a reflective element beneath the hemi-spherical array such that it reflects the light substantially back towards the direction of origin of the light rays. This may be achieved by a reflective element which incorporates an array of approximately spherical indentations. The approximately spherical indentations each has a radius of curvature that substantially coincides with the center of curvature of the hemi-sphere located directly above it. The invention described in this application is directed to “recycling” of such light rays in a semi-retro-reflective manner to enhance the brightness in TIR-based displays. Furthermore, the invention described enables high efficiency and high color saturation in a reflective color display comprising of a color filter array.